bit of tabs, bit of learn-by-ear. tabs for the real tricky buits only, mostly. i always try and do it by ear primarily, it helps further develop your ear for that sort of thing. But if its a fairly quick solo, i'll just get tabs.
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My ear is terrible, I haven't spent much time developing it. I usually use tabs, or sheet music. Learning by sheet music is best though. It's easier to memorize the song after learning by sheet music.
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depends, if the assignment is to figure it out by ear, i will.
if i''ve got the sheetmusic, i won't play it by ear
if i don't, or am too lazy to seek it, or just want to have some fun, or improve my ear, i'll play it by ear..

playing it by ear multiplies how much you learn from playing a song by a big number, so that's what i started to do some years back, as an exercise, and by checking afterwards with the sheetmusic , you can analyse your mistakes and focus on those (so if i find i can't notate the timing all too well, i'll work on that, if i miss or don't get a modulation, i'll have a look at that etc.
so that's actually using both sheet and ear.. another combination i like to use is looking at the sheetmusic, not memorising the notes (or maybe the key), but memorising how it sounds, then play it, or what i remember from it, and then listen to the song, and play along..

if i use sheetmusic as standard notation or tabs depends on what i want to find out, playing a song can do both, so i see what one's most available, but if i want to analyse a song, i definitely want standard notation

thing is, pretty much the only place to get tabs easier than standard notation, is on the internet, like this site, and those tabs are so often so wrong, and i thus haven't used them for ages now..

anyway, ear's always the best for me
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yea, I always try to learn stuff by ear, but I just learned Gunshot to the head of trepidation by ear, and the only thing I'm having trouble with is figuring out the solo. Should I just check tabs?
You don't really need any music theory background to learn tabs. I would say 80% prefer tabs cause of it's simplicity